The quadratic equation 5x^2 + 3x - 2 = 0 has roots that can be expressed in whic

The quadratic equation 5x^2 + 3x - 2 = 0 has roots that can be expressed in which form? (2023)

The quadratic equation 5x^2 + 3x - 2 = 0 has roots that can be expressed in which form? (2023)

Step 1: Identify the quadratic equation, which is 5x^2 + 3x - 2 = 0.
Step 2: Recognize the standard form of a quadratic equation, which is ax^2 + bx + c = 0, where a = 5, b = 3, and c = -2.
Step 3: Calculate the discriminant using the formula D = b^2 - 4ac.
Step 4: Substitute the values of a, b, and c into the discriminant formula: D = 3^2 - 4*5*(-2).
Step 5: Calculate 3^2, which is 9.
Step 6: Calculate 4*5*(-2), which is -40, so we have D = 9 + 40.
Step 7: Add 9 and 40 to get D = 49.
Step 8: Determine if the discriminant is a perfect square. Since 49 is 7^2, it is a perfect square.
Step 9: Conclude that because the discriminant is a perfect square, the roots of the quadratic equation are rational.

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